Question

digging deeper

1. determine the height above the ground, ( h ), of julie’s kite using

the following diagram. round to one decimal place.
diagram of a kite, a girl, a fence, and a boat
we know
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Explanation:

Step1: Use the tangent function for the right - triangle part

In the right - triangle with angle \(15^{\circ}\) and adjacent side \(25m\), we know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 15^{\circ}\) and the adjacent side \(x = 25m\). Let the height of the triangle part be \(h_1\). So, \(\tan(15^{\circ})=\frac{h_1}{25}\). Since \(\tan(15^{\circ})=2 - \sqrt{3}\approx0.2679\), then \(h_1=25\times\tan(15^{\circ})\).

Step2: Calculate \(h_1\)

\(h_1 = 25\times0.2679=6.6975m\)

Step3: Calculate the total height \(h\)

The total height \(h=h_1 + h_2\), where \(h_2 = 1.2m\). So \(h=6.6975+1.2\)

Step4: Round the result

\(h=7.8975\approx7.9m\)

Answer:

\(7.9m\)